OFFSET
0,3
COMMENTS
Arises in connection with the expansion (e i)^(Pi i) = e^(Pi i) * i^(Pi i) = -1 * exp(Pi i log i) = -exp(Pi i * Pi/2 i) = -exp(-Pi^2/2) = -0.00719188335582636560780136639...
One has to be careful about branches of multivalued complex functions. By definition (e i)^(Pi i) is exp(Pi i log(e i)) [using any of the branches of log] = exp(Pi i (1 + Pi i/2 + 2 n Pi i)) [ for any integer n ] = - exp(- Pi^2/2 - 2 n Pi^2). There is no imaginary part in any of its branches. If n=0 we get (-1) times the present constant.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
EXAMPLE
.0071918833558263656078013663963712029553623180815979475580371...
MATHEMATICA
Join[{0, 0}, RealDigits[Exp[-Pi^2/2], 10, 120][[1]]] (* Harvey P. Dale, Jul 11 2011 *)
PROG
(PARI) exp(-Pi^2/2) \\ Charles R Greathouse IV, Mar 25 2014
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
N. J. A. Sloane, Aug 06 2010, based on postings to the Sequence Fans Mailing List by Alonso Del Arte, Charles R Greathouse IV, Sean A. Irvine, Robert Israel and other correspondents.
STATUS
approved